I guess is not about be responsible for other people`s coin. MyEtherWallet allows to store a local, light client wallet connected to an external node. This way you have your loca, safe wallet (because you old you private key), but you can access the blockchain without need to host the node.
So why SIA-UI (client) need to install SIA (The node) also?
How ca we configure SIA-UI (client) to connect to a external node?

@pynetx , @torreslabs
There is a significant difference in sia and for example ethereum blockchain.
For ethereum anyone can look at etherchain.org and see the balance of any ethereum address. Ethereum is just a public distributed ledger. So, a node is not bound to a particular wallet or address.
A Sia node has access only to balance of one wallet- the one that is unlocked. A wallet has many different addresses, but the balance is the total sum of all addresses belonging to the wallet. So it is more private. Public are only transactions to a particular address, not the total balance.

There are problems operating one wallet on more than one host simultaneously, as the file services are bound to nodes.
Maybe there will be a solution allowing syncing/sharing a wallet between nodes, but that is not the case yet. The main goal for Sia is to operate the m2m storage exchange. And for that it is essential to have the storing/renting nodes as single instances. Having mirroring between nodes would unnecessary complicate the network operation. There is enough missing critical functionality already that has to be implemented. Let's put node mirroring and wallet sharing somewhere in a future roadmap as that is more "nice to have" than "critical operation".

@reinisp thanks for your clear explanation. It helps me a lot.
One question. In my case, the main idea to have a web wallet, is to provide many diferents wallets for a single node.
The idea is to have one SIA service (for a private application), where more than one user can use this node to upload and download files.
So in this case is more about connect the wallet with a single remote node.